Error establishing a database connection only in wp-admin

I have my site running locally and on Heroku. It works locally, but on Heroku, when I try to go to site admin (/wp-admin), it gives me this:

Error establishing a database connection
This either means that the username and password information in your wp-config.php file is incorrect or we can’t contact the database server at [my host on Heroku]. This could mean your host’s database server is down.

Are you sure you have the correct username and password?
Are you sure that you have typed the correct hostname?
Are you sure that the database server is running?
If you’re unsure what these terms mean you should probably contact your host. If you still need help you can always visit the WordPress Support Forums.

I double-checked my Heroku environment variables which contain the database name, host, username, and password, and they are all correct. The front end of the site works, but the admin areas don’t.